Prediction Models in Configural Frequency Analysis

Configural frequency analysis models are presented for predicting a discrete criterion variable from combining 2 or more discrete predictor variables nonparametrically. Predictions are made via so-called prediction types which allow to predict a criterion class from combined predictor classes. Prediction types are implicitely defined as cells of a 2-dimensional contingeney table with rows as predictor combinations and columns as criterion classes. The CFA is extended for two criteria, and for stratified sampling.     

Orthogonal Prediction Configural Frequency Analysis by Chi-Square Partitioning

Prediction Configural Frequency Analysis is reconceptualized in terms of orthogonal Chi-Square decomposition. The predictor-criterion contingency table is subdivided into fourfold tables. The chisquare components of these tables, calculated using Kimball's shortcut formulas, sum up to the total chi-square of the r × c table. As a result of this decomposition, the number of r × c prediction tests of classical Prediction CFA is reduced to R = (r - 1) (c - 1) biprediction types. The resulting version of Prediction CFA is termed orthogonal Prediction CFA. Orthogonal Prediction CFA is illustrated using data describing pupils' performance in German language as predicted from performance in two verbal tests.     

Normal Approximations of Exact Tests in Configural Frequency Analysis

The most common tests for types and antitypes in configural frequency analysis are normal approximations of exact tests. In the paper such statistics under the complete independence model and under the fixed margins model are discussed. It turns out that these test statistics are not acceptable when the number of simultaneously performed tests is large or when the expected frequencies are small. In these cases, the use of exact tests is advocated and some existing computer programs for such tests are indicated. A normal approximation based on the strong version of the De Moivre-Laplace limit theorem is also discussed. Empirical examples are given from longitudinal data describing psychological development of boys.     

A More Powerful Simultaneous Test Procedure in Configural Frequency Analysis

In the Configural Frequency Analysis (CFA) of KRAUTH and LIENERT (1973 a, b), overfrequented (or underfrequented) cells in multivariate contingency tables are identified by simultaneous binomial tests. As an alternative, finite and asymptotic tests are proposed, which are derived from the (exact conditional) generalized hypergeometrical distribution of the cell frequencies. These tests allow for considerably more powerful decisions than do the conservative binomial tests.     

Response Curve Comparison by Pseudo-Multivariate Two-Sample Configural Frequency Analysis

This paper introduces pseudo-multivariate Configural Frequency Analysis (CFA) for comparison of time series from two independent samples. The method extends application of standard two-sample CFA, bi-prediction CFA, and longitudinal CFA. Methods for identification of uni-discrimination types and bi-discrimination types are proposed. The pseudo-multivariate CFA is applied to sets of response curves from two independent samples of rats. The experimental group of rats was exposed to a stressful noise condition. The control group was not exposed to stress. Amount of food intake was measured over five days. Longitudinal discrimination types suggest that, under stress, rats reduce food intake at first, increase intake as habituation to stress increases, and show greater day-to-day variability of intake.     

Evaluating Chessboard MANOVA Designs Using Predictive and Matching Configural Frequency Analysis

This paper concerns the nonparametric evaluation of chessboard MANOVA designs. For this purpose, a matching procedure based on rook methodology is suggested as a complement to predictive coafigural frequency analysis. Using this procedure, a multivariate hypothesis can be tested in a single test. It is also possible to design a significance test to fit a specific composite hypothesis. The procedure is illustrated by results from a multivariate psychopharmacological experiment in which the effects of alcohol and caffeine were studied on test performance and volatility.     

The General Linear Model as a Framework for Models in Configural Frequency Analysis

The present paper discusses models of Configural Frequency Analysis (CFA). For most models of CFA maximum likelihood estimators are given. For all of these models least squares estimators are also given. These estimators are equivalent to each other if quasiparametric conditions prevail. Using the second approach, the general linear model can be used to systematize CFA models. Numerical examples are given, using both artificial and psychiatric data.     

A Note on a Continuity Correction for Testing in Three-Dimensional Configural Frequency Analysis

A continuity correction is proposed for the test statistics of HABERMAN (1978) and LEHMACHER (1981) for identifying overfrequented (or underfrequented) cells in the three-dimensional Configural Frequency Analysis (CFA). Its quality is shown by comparison with the test based on the exact distribution of the cell frequencies.     

Test Procedures in Configural Frequency Analysis (CFA) Controlling the Local and Multiple Level

The test statistics used until now in the CFA have been developed under the assumption of the overall hypothesis of total independence. Therefore, the multiple test procedures based on these statistics are really only different tests of the overall hypothesis. If one likes to test a special cell hypothesis, one should only assume that this hypothesis is true and not the whole overall hypothesis. Such cell tests can then be used as elements of a multiple test procedure. In this paper it is shown that the usual test procedures can be very anticonservative (except of the two-dimensional, and, for some procedures, the three-dimensional case), and corrected test procedures are developed. Furthermore, for the construction of multiple tests controlling the multiple level, modifications of Holm's (1979) procedure are proposed which lead to sharper results than his general procedure and can also be performed very easily.     

Predictive Configural Frequency Analysis Evaluated by Simultaneous Berchtold-Corrected Fourfold X2-Tests

For testing against outlying cells in r × c contingency tables in predictive configural frequency analysis, it is suggested not to replace the usual PEARSON fourfold X²-test by YATES ' discontinuity corrected test but by BERCHTOLD'S test correcting for skewed hypergeometric distributions. In general, the BERCHTOLD correction is most efficient for tables involving three small and one large fourfold frequency. The correction is illustrated by configural frequency analysis of data from psychotherapy research.     

Configural Frequency Analysis as a Parametric Method for the Search of Types and Antitypes

The article introduces Parametric Configural Frequency Analysis (CFA). It is argued that there are two types of parameters that can be of importance in CFA models. The first is effect parameters that are estimated from the data. This type of parameter is involved in almost all models of Classical, nonparametric CFA. The second type involves a priori or distributional parameters that can be used for estimation of expected frequencies. These parameters are specified a priori rather than estimated from data. A combination of models from Classical CFA and Parametric CFA is introduced as Semi-Parametric CFA. Data examples illustrate the new CFA models in comparison with the Classical CFA. Interpretational issues are discussed.     

Nonparametric Comparison of Longitudinal Response Patterns from Unpaired Samples Using Configural Frequency Analysis

Nonparametric methods of Configural Frequency Analysis (CFA) for the comparison of longitudinal response patterns are discussed. In particular, methods of transforming response patterns into profiles that can be analyzed using CFA are presented. When two independent samples are given, two sample CFA can be applied to perform local testing. An example is given from research on obesity. Two sample CFA of response pattern is compared to methods of global testing.     

Nonparametric Comparison of Longitudinal Response Patterns from Paired Samples Using Configural Frequency Analysis

Nonparametric methods of Configural Frequency Analysis (CFA) for comparing longitudinal response patterns are discussed. Characteristics of diagonally symmetric frequency distributions are mapped with hypotheses on the locus of treatment effects. Test statistics for the analysis of local dependencies are discussed. In particular, applications to paired samples are considered. A biomedical example is given from research on the effects of spasmolytic drugs. Local CFA-testing is compared with global testing. Alternative strategies of testing and the respective underlying assumptions are discussed.     

Catecholamine Response Curves of Male Hypertensives Identified by Lehmacher's Two Sample Configural Frequency Analysis

A new application of LEHMACHER'S (1980) marginal homogeneity sign tests is given by analysis of bivariate response curves (or response surfaces) in two unpaired samples of hypertensive versus normotensive patients. Rationale and computations are illustrated by empirical data from sympathomedullary stress research.     

Temporal Patterns of Variable Relationships in Person-Oriented Research: Prediction and Auto-Association Models of Configural Frequency Analysis

Longitudinal Configural Frequency Analysis (CFA) seeks to identify, at the manifest variable level, those temporal patterns that are observed more frequently (CFA types) or less frequently (CFA antitypes) than expected with reference to a base model. This article discusses, compares, and extends two base models of interest in longitudinal data analysis. The first of these, Prediction CFA (P-CFA), is a base model that can be used in the configural analysis of both cross-sectional and longitudinal data. This model takes the associations among predictors and among criteria into account. The second base model, Auto-Association CFA (A-CFA), was specifically designed for longitudinal data. This model takes the auto-associations among repeatedly observed variables into account. Both models are extended to accommodate covariates, for example, stratification variables. Application examples are given using data from a longitudinal study of domestic violence. It is illustrated that CFA is able to yield results that are not redundant with results from log-linear modeling or multinomial regression. It is concluded that CFA is particularly useful in the context of person-oriented research.     

Configural Frequency Analysis (CFA) Revisited — a New Look at an Old Approach

Configural frequency analysis (CFA) is a widely used method for the identification of types and syndromes in contingency tables. However, the type model of CFA shows some major deficiencies. In this paper, we propose an alternative modeling of types eliminating the shortcomings of CFA. Basically, a type is modeled as a combination of traits or symptoms that deviates from the pattern of association holding true for the complementary configurations of the contingency table. The new approach is formulated in terms of a log-linear model. It is shown that parameter estimation can be performed with methods known from the analysis of incomplete contingency tables. Test procedures for confirmatory analysis and methods for exploratory search for type configurations are developed. We illustrate the methodology with two practical examples.     

Partial Distributional Canonical Discriminant Analysis

A canonical discriminant technique is proposed which is unrelated to particular distributional assumptions. This approach allows for a data generated choice between ordered, partially ordered and unordered outcomes and remains identifiable in each dimension of the canonical model. The concepts of allocatability and distinguishability of categories are investigated. Maximum likelihood parameter estimation is conducted and inferential tests for the assessment of the dimensionality of the canonical model are derived. The model is applied to the perioperative prediction of risk of death from peritonitis, using real data.     

Quantitative Methods for the Analysis of Equine Locomotion and Their Applications to Other Species

SYNOPSIS. Although the methods discussed in this report havebeen applied to biomechanical studies on horses, these techniqueshave broad applications to locomotor research on all species.Cinematography has been and will continue to be the most widelyapplied of these methods. Recent advances in video imaging willcomplement, but not completely replace, this technique. Electrogoniometryhas been primarily restricted to use on human beings and horses.This method has far broader kinematic applications and its useshould be seriously investigated by researchers studying otherspecies. Force plates have been used widely, and with the advancesin research technology, even broader applications of this techniquewill be available. The technology used in the development ofthe instrumented shoes can be used to develop instrumentationfor investigations in other species. Substantial modificationsincluding the miniaturization of electrical components willbe necessary. The references cited in this discussion, although in no wayall-inclusive, indicate that a vast amount of research usinga variety of methods has been conducted on the locomotion ofanimals. We have just begun to define and understand the complexinteractions of the musculoskeletal system with other body systems.Students of locomotion must use their imagination and ingenuityin refining and adapting these techniques, and in developingnew methods to solve the many unanswered questions.